Modeling Fluid Structure Interaction over a Flexible Fin Attached to a NACA0012 Airfoil

181 Pages·2015·2.13 MB·English

by  Srinivasa Ravindra Pantula

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Dissertations Graduate College
12-2008
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Srinivasa Ravindra Pantula
Western Michigan University
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Pantula, Srinivasa Ravindra, "Modeling Fluid Structure Interaction over a Flexible Fin Attached to a
NACA0012 Airfoil" (2008). Dissertations. 803.
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MODELING FLUID STRUCTURE INTERACTION OVER A FLEXIBLE FIN
ATTACHED TO A NACA0 012 AIRFOIL
by
Srinivasa Ravindra Pantula
A Dissertation
Submitted to the
Faculty of The Graduate College
in partial fulfillment of the
requirements for the
Degree of Doctor of Philosophy
Department of Mechanical and Aeronautical Engineering
Advisor: Dr. William Liou
Western Michigan University
Kalamazoo, Michigan
December 2008
UMI Number: 3340195
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Copyright by
Srinivasa Ravindra Pantula
2008
ACKNOWLEDGMENTS
I would like to thank my Professor Dr. William Liou
for his for his brilliant guidance, great innovative
ideas and constant help through out of my thesis. I would
like to thank each of my committee members, Dr. Tianshu
Liu and Dr. Iskender Sahin of Western Michigan University
and Dr. Ray Hixon of University of Toledo for their in
terest, enthusiasm and wonderful guidance through out my
thesis.
This research project was supported by the Air Force
Office of Scientific Research (AFOSR). Thanks to AFOSR
for their support.
I am very fortunate to be working at the computation
engineering physics laboratory of the Mechanical and
Aeronautical engineering department along side Dr. Meng
Huang Lu, Dr. Yang Yang and soon to be doctor yongqing
Peng. I am thankful to Dr. Meng Huang Lu for providing me
with his fluid solver and helping me in understanding the
code. I am also thankful to Dr. Yang Yang for proving me
with a structural solver and helping me modify his code
according to my needs. Yongqing Peng and I shared some
graduate classes together and it was great to study and
ii
Acknowledgments—continued
work with him. I would like to thank him for the wonder
ful discussions we had day in and day out. I would also
like to thank Dr. Javier Montefort for his help through
out my thesis in providing me with the processed experi
mental data when ever needed. I am very thankful for the
long discussions and those free invitations to view expe
riments. I would also like to thank Dr. Parviz Merathi
and all other people at the Fluids lab. My thanks to all
of my other friends at Western Michigan University and
especially the volleyball gang for making my life at WMU
very enjoyable.
Finally I would like to thank my mother, Rajeswari
Pantula and my sister, Usha Pantula for their constant
support, encouragement and care all these years. Without
them any of my accomplishments are not possible. I would
like to dedicate this work to the memory of my late fa
ther Chandra Sekhar Rao Pantula.
Srinivasa Ravindra Pantula
iii
TABLE OF CONTENTS
ACKNOWLEDGMENTS ii
LIST OF FIGURES vii
CHAPTER
I. INTRODUCTION 1
1.1 Motivation 1
1.2 Basic design 2
1.3 Fluid structure interactions 4
1.4 Numerical representation of FSI problem .. 9
1.5 Literature review of immersed boundary
methods 11
1.6 Manuscript organization 13
II. THE NAVIER STOKES FINITE DIFFERENCE FLUID
DYNAMIC SOLVER 17
2.1 Transforming Cartesian to curvilinear
coordinates 18
2.2 Spatial discretization of continuity
and momentum equations 27
2.3 Reynolds stress modeling 3 2
2.4 Temporal discretization of continuity
and momentum equations 3 9
III. THE SUBDIVISION FINITE ELEMENT STRUCTURAL
DYNAMIC SOLVER 41
3.1 Basic formulation 41
3.2 Finite element discretization 47
iv
Table of Contents—continued
CHAPTER
IV. IMMERSED BOUNDARY METHODS 52
4.1 Non-boundary conforming methods 52
4.2 Treatment of immersed boundary (boun
dary reconstruction) 57
V. VALIDATION OF THE FLUID DYNAMIC AND STRUCTURAL
DYNAMIC SOLVERS 66
5.1 Turbulent flow over a NACA0012 airfoil
(body-fitted coordinates) 67
5.2 Unsteady deflection of a simply sup
ported square plate 75
VI. VALIDATION OF THE FINITE DIFFERENCE IMMERSED
BOUNDARY NAVIER-STOKES SOLVER 78
6.1 Flow over a circular cylinder 80
6.2 Laminar flow over a NACA0012 airfoil 85
6.3 Unsteady flow over a circular cylinder
at Reynolds number of 200 90
6.4 Turbulent flow over a NACA0012 airfoil
at Reynolds number of 170000 96
6.5 Laminar flow over an infinitesimally
thin flat plate 101
6.6 Flow over a flapping flat plate using
immersed boundary method 105
VII. FLUID STRUCTURE INTERACTION OVER A PASSIVE
FLEXIBLE FLAT PLATE 121
7.1 Problem description 122
7.2 Computation domain 123
7.3 Coupling CFD and CSD solvers 126
7.4 Results and discussions 129
v
Table of Contents—continued
CHAPTER
VIII. MODELING FLUID STRUCTURE INTERACTION OVER A
FLEXIBLE FIN ATTACHED TO THE UPPER SURFACE OF
A NACA0012 AIRFOIL 138
8.1 Experimental set-up 13 9
8.2 Computational set-up 14 0
8.3 Domain and grid details 141
8.4 Results and discussion 145
IX. CONCLUSIONS AND FUTURE DIRECTIONS 157
BIBLIOGRAPHY 162
VI
LIST OF FIGURES
1.1. Flexible fin attached to a NACA0012 airfoil .... 3
1.2. One-way coupling vs. two-way coupling 5
1.3. Numerical representation of the FSI problem .... 10
3.1. Shell geometry in the reference (left) and
deformed (right) configuration 42
4.1. Classification of non-boundary conforming me
thods 53
4.2. Schematic interpretation of one-direction li
near interpolation for solid boundary with
finite thickness 59
4.3. Linear interpolation technique for forcing at
one grid point 60
4.4. Two-sided one-direction interpolation tech
nique 63
4.5. Two-direction one-sided interpolation tech
nique 64
5.1. C-type computational grid with nodes of
200*95 68
5.2. Close up of the body-fitted C-grid with a
NACA0012 airfoil 69
5.3. Grid independence study by comparing surface
pressure distributions 71
5.4. Pressure contours for three different angles
of attack . . 73
5.5. Lift coefficient curve for different angels
of attack for a NACA0012 airfoil . 74
5.6. Drag coefficient computed at different angles
of attack 75
5.7. Time variation of central deflection of a
simply supported plate 7 7
vii